p-Determinants and monodromy of differential operators

TL;DR

This paper demonstrates that p-determinants of specific differential operators can be lifted to rational power series and relates these series to the monodromy of the operators, providing a new computational approach.

Contribution

It introduces a method to lift p-determinants to power series over rationals and connects these to monodromy, advancing understanding of differential operators in algebraic geometry.

Findings

p-determinants can be lifted to power series over ield

Power series are computed via monodromy of differential operators

Provides a new computational framework for differential operators

Abstract

We prove that $p$-determinants of a certain class of differential operators can be lifted to power series over $\mathbb{Q}$. We compute these power series in terms of monodromy of the corresponding differential operators.